# A firm model with strict regulation and management influence on profit

### Abstract

We propose and investigate a firm model in the form of an optimal control problem, where the optimal control criterion is the total profit over a finite period (the integral of the profit function over a finite time interval). We consider the profit function as the difference between the revenue and cost functions, where the revenue function is determined by a neoclassical production function and the cost function is a solution to some auxiliary problem. Some additional restrictions on the production function and conditions of the auxiliary problem for the cost function take into account the impact of management practice and government regulations of firms. In particular, we assume that the management affects the output as well as costs, while the profit maximization is achieved by optimal distribution of the management between them. We establish some properties of solutions to the optimal control problem using the Pontryagin maximum principle. In particular, it was shown that the optimal control has the zero regime in the final stage. Also, we found sharp conditions under which the optimal control is zero at any time.

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*Mathematical notes of NEFU*, 27(2), pp. 39-53. doi: https://doi.org/10.25587/SVFU.2020.56.60.003.

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